Problem
Research questions and friction points this paper is trying to address.
online coverage
drone
competitive ratio
line barrier
mobile sensor
Online Drone Coverage of Targets on a Line
🤖 AI Summary
This study addresses the online coverage problem for a drone tasked with monitoring dynamically appearing targets on a line while minimizing its total trajectory length. The drone is equipped with a sensor of fixed field-of-view angle α and must continuously reposition itself in real time to ensure all active targets remain covered. The authors propose three online algorithms, among which the FA algorithm significantly outperforms existing approaches when π/6 < α < π/3. Theoretical analysis shows that FA achieves a competitive ratio of 1.25 at α = π/4, improving upon the baseline √2. Furthermore, they establish a lower bound of (1+√2)/2 ≈ 1.207 on the optimal competitive ratio for α ∈ [0, π/4]. By integrating geometric coverage modeling with competitive analysis, this work advances both algorithmic design and theoretical understanding of online coverage problems.
📝 Abstract
We study a problem of online targets coverage by a drone or a sensor that is equipped with a camera or an antenna of fixed half-angle of view $α$. The targets to be monitored appear at arbitrary positions on a line barrier in an online manner. When a new target appears, the drone has to move to a location that covers the newly arrived target, as well as already existing targets. The objective is to design a coverage algorithm that optimizes the total length of the drone's trajectory. Our results are reported in terms of an algorithm's competitive ratio, i.e., the worst-case ratio (over all inputs) of its cost to that of an optimal offline algorithm.
In terms of upper bounds, we present three online algorithms and prove bounds on their competitive ratios for every $α\in [0, π/2]$. The best of them, called \FA is significantly better than the other two for $π/6 < α< π/3$. In particular, for $α=π/4$, its worst case, \FA has competitive ratio $1.25$, while the other two have competitive ratio $\sqrt{2}$. Finally, we prove a lower bound on the competitive ratio of online algorithms for a drone with half-angle $α\in [0, π/4]$; this bound is a function of $α$ that achieves its maximum value at $α= π/4$ equal to $(1+\sqrt{2})/2 \approx 1.207$.
Innovation
Methods, ideas, or system contributions that make the work stand out.
online algorithm
competitive ratio
drone coverage
line barrier
field of view
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